Binary Tree Level Order Traversal II (Bottom-up)
Given the root of a binary tree, return the bottom-up level order traversal of its nodes' values. Use BFS and reverse the final result.
Why Interviewers Ask This
Interviewers at Airbnb ask this to verify your mastery of Breadth-First Search (BFS) and queue manipulation. They specifically test if you can handle level-by-level processing and understand how to reverse the output order efficiently without compromising time complexity. This assesses your ability to solve standard tree problems with a slight variation, ensuring you don't just memorize solutions but adapt algorithms logically.
How to Answer This Question
1. Clarify requirements: Confirm input is a root node and define 'bottom-up' as starting from the deepest leaf level up to the root. 2. Select Data Structure: Explicitly state you will use a Queue for BFS to process nodes level by level, ensuring O(N) time complexity. 3. Implement Standard BFS: Describe iterating through the current queue size to isolate each level, collecting values into a temporary list. 4. Handle Reversal: Explain that instead of complex logic during traversal, you will simply reverse the final list of lists after the loop completes. 5. Analyze Complexity: Conclude by stating the solution runs in O(N) time and O(N) space, referencing Airbnb's focus on scalable performance even for easy questions.
Key Points to Cover
- Explicitly mentioning the use of a Queue for BFS demonstrates fundamental algorithmic knowledge
- Explaining the level-by-level iteration logic proves understanding of tree traversal mechanics
- Choosing to reverse the list post-traversal shows awareness of efficient coding practices over complex insertion logic
- Stating O(N) time and space complexity confirms ability to analyze algorithmic performance
- Clarifying edge cases like empty trees or single-node trees shows attention to detail
Sample Answer
To solve the bottom-up level order traversal, I would first clarify that we need to return levels starting from the leaves up to the root. My approach involves using a standard Breadth-First Search strategy with a queue data structure. I'll initialize a queue with the root node and an empty result list. While the queue isn't empty, I determine the number of nodes currently in the queue, which represents the width of the current level. I then iterate exactly that many times, dequeuing each node, adding its value to a temporary level list, and enqueuing any non-null children. Once the inner loop finishes, I append the collected level list to my main result array. After the outer loop completes, the result contains levels from top to bottom. To achieve the required bottom-up order, I will simply reverse the entire result list before returning it. This ensures the deepest level appears first. This method maintains an optimal O(N) time complexity since we visit every node once, and O(N) space for the queue and output. At Airbnb, where efficiency matters, this approach guarantees we handle large tree structures without unnecessary computational overhead or complex recursive depth issues.
Common Mistakes to Avoid
- Using recursion which leads to stack overflow risks on deep trees instead of iterative BFS
- Attempting to insert each level at the beginning of the result list causing O(N^2) time complexity
- Failing to handle null root inputs or empty trees resulting in runtime errors
- Confusing bottom-up traversal with pre-order or post-order depth-first search approaches
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